Reduce to lowest terms: $- \dfrac{9}{2} \div - \dfrac{4}{9} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{4}{9}$ is $- \dfrac{9}{4}$ Therefore: $ - \dfrac{9}{2} \div - \dfrac{4}{9} = - \dfrac{9}{2} \times - \dfrac{9}{4} $ $ \phantom{- \dfrac{9}{2} \times - \dfrac{9}{4}} = \dfrac{-9 \times -9}{2 \times 4} $ $ \phantom{- \dfrac{9}{2} \times - \dfrac{9}{4}} = \dfrac{81}{8} $